1
00:00:00 --> 00:00:10
So, let's start with where we were.
We were talking about exponential
2
00:00:10 --> 00:00:20
growth in populations.
And, we said we could describe this
3
00:00:20 --> 00:00:31
as one over the dN/dt equals some
growth rate, r.
4
00:00:31 --> 00:00:40
And, in this case,
we're talking about,
5
00:00:40 --> 00:00:50
let me ask that is a question.
As a model for population growth,
6
00:00:50 --> 00:01:00
what's wrong with this? What does
this project?
7
00:01:00 --> 00:01:06
This is N. This is time.
There's no stopping it. I mean,
8
00:01:06 --> 00:01:13
we'd be knee deep in everything if
populations grew according to this
9
00:01:13 --> 00:01:19
model, OK, because it just goes off
into infinity in terms of density.
10
00:01:19 --> 00:01:26
So, we know that this is inadequate.
In fact, some people describe the
11
00:01:26 --> 00:01:33
entire field of population ecology
as a field that tries to determine
12
00:01:33 --> 00:01:40
why real populations can't grow
according to this model.
13
00:01:40 --> 00:01:45
In other words,
the whole field is trying to
14
00:01:45 --> 00:01:50
understand what the mechanisms are
in populations that limit their
15
00:01:50 --> 00:01:55
growth. So, they don't grow
exponentially forever.
16
00:01:55 --> 00:02:00
So, in this case, this is really a
maximum growth rate.
17
00:02:00 --> 00:02:06
We can call that r Max.
And in this case, it's a constant.
18
00:02:06 --> 00:02:12
So, when we're talking about
exponential growth,
19
00:02:12 --> 00:02:19
the growth rate per unit time is the
maximum growth rate that that
20
00:02:19 --> 00:02:25
population is capable of under those
conditions and it's a constant.
21
00:02:25 --> 00:02:31
So, if we want to plot it this way,
one over N, dN/dt, as a function of
22
00:02:31 --> 00:02:39
N, is constant.
It doesn't change as density changes.
23
00:02:39 --> 00:02:48
So, now we're going to take a
historical look at this.
24
00:02:48 --> 00:02:58
Back in the 1920s, two fellows
named Pearl and Reed wanted to model
25
00:02:58 --> 00:03:05
human population growth.
And they looked at this exponential
26
00:03:05 --> 00:03:11
growth equation,
and they said there's got to be
27
00:03:11 --> 00:03:16
something wrong with that.
We can't just apply that to humans,
28
00:03:16 --> 00:03:22
although if they plotted as a
function of time,
29
00:03:22 --> 00:03:27
and this is humans in the US from
1800 to 1900, and this is the human
30
00:03:27 --> 00:03:33
population size,
if they plotted this on this curve,
31
00:03:33 --> 00:03:39
they got something that looked like
this.
32
00:03:39 --> 00:03:46
So, it kind of looked like
exponential growth.
33
00:03:46 --> 00:03:53
But, when they went in it actually
looked at one over ND,
34
00:03:53 --> 00:04:01
dN/dt, which would be the slope
along here, they found that it looks
35
00:04:01 --> 00:04:07
something like this.
In other words,
36
00:04:07 --> 00:04:11
the actual growth rate of the
population was decreasing as the
37
00:04:11 --> 00:04:15
number of humans increased.
And this is called a density
38
00:04:15 --> 00:04:28
dependent response.
39
00:04:28 --> 00:04:35
OK, so if we look at this,
remember from last time that r is
40
00:04:35 --> 00:04:42
equal to the birth rate minus the
death rate, right?
41
00:04:42 --> 00:04:49
So, we can look at,
this is just a simple cartoon
42
00:04:49 --> 00:04:56
drawing of what's going on here.
Density dependent factors regulate
43
00:04:56 --> 00:05:02
population size.
So, if we plot one over ND,
44
00:05:02 --> 00:05:06
dN/dt as either a birth rate or a
death rate, as a function of
45
00:05:06 --> 00:05:10
population density,
when you have density,
46
00:05:10 --> 00:05:15
really the one that's the most
important here is looking at this
47
00:05:15 --> 00:05:19
one, that death rate increases as
population increases,
48
00:05:19 --> 00:05:24
and birth rate decreases.
And you have an intersection here
49
00:05:24 --> 00:05:28
where birth rate and death rate are
equal, and your population's going
50
00:05:28 --> 00:05:33
to stabilize there where there will
be no change in population growth.
51
00:05:33 --> 00:05:39
And these density dependent birth
rates and death rates introduce a
52
00:05:39 --> 00:05:46
stabilizing factor.
As N increases, r decreases in the
53
00:05:46 --> 00:05:53
population. And that's what brings
population back into some sort of
54
00:05:53 --> 00:06:00
equilibrium. OK, so all
right, forget that.
55
00:06:00 --> 00:06:06
So, let's go back over to Pearl and
Reed. We're going to stay on the
56
00:06:06 --> 00:06:12
board for awhile.
So the question is,
57
00:06:12 --> 00:06:18
how do we modify that equation,
our simple exponential growth
58
00:06:18 --> 00:06:24
equation, so that it more
realistically describes real
59
00:06:24 --> 00:06:30
populations that can't grow totally
unconstrained?
60
00:06:30 --> 00:06:44
So what Pearl and Reed did,
how do we modify the exponential
61
00:06:44 --> 00:06:59
growth? So, here's what we want the
characteristics to be of this
62
00:06:59 --> 00:07:14
equation. We want one over N,
dN/dt, to go to zero as N gets large.
63
00:07:14 --> 00:07:19
And we want it to go to our max,
the maximum growth rate, when N
64
00:07:19 --> 00:07:24
approaches zero.
In other words, at really,
65
00:07:24 --> 00:07:29
really low population density is,
you can effectively have exponential
66
00:07:29 --> 00:07:34
growth because nothing's
limiting you.
67
00:07:34 --> 00:07:41
When the density gets very,
very large, you want this growth
68
00:07:41 --> 00:07:48
rate to go to zero.
So, they came up, so let's plot
69
00:07:48 --> 00:07:56
this N. This is T,
and here's our exponential growth
70
00:07:56 --> 00:08:06
equation.
And they came up with a function
71
00:08:06 --> 00:08:19
that looks like this.
So, this would be one over N,
72
00:08:19 --> 00:08:32
and to describe this, we have this
equation.
73
00:08:32 --> 00:08:37
And this is called the logistic
equation for reasons that are
74
00:08:37 --> 00:08:42
historically obscure.
This is a French term that has
75
00:08:42 --> 00:08:47
something to do with,
anybody know, who speaks French?
76
00:08:47 --> 00:08:52
It has to do with something
military. Anyway,
77
00:08:52 --> 00:08:57
I've never been able to figure out
why they call this the
78
00:08:57 --> 00:09:05
logistic equation.
But it doesn't matter what it's
79
00:09:05 --> 00:09:15
called, this is what it is.
And K here is the carrying capacity
80
00:09:15 --> 00:09:26
of the environment.
It's the maximum number of
81
00:09:26 --> 00:09:37
organisms were the population
levels off, OK?
82
00:09:37 --> 00:09:44
All right, so let's look at this.
Let's replot this, because it's
83
00:09:44 --> 00:09:52
easier to analyze the features.
We're going to plot one over N,
84
00:09:52 --> 00:10:00
dN/dt as a function of N. If we
want to rewrite the equation,
85
00:10:00 --> 00:10:08
one over N, dN/dt equals our max.
86
00:10:08 --> 00:10:20
We're just rearranging that equation
to make it easier to visualize.
87
00:10:20 --> 00:10:32
OK? So that we have a line that we
can put that on,
88
00:10:32 --> 00:10:45
such that K is the X intercept,
and what's this?
89
00:10:45 --> 00:10:57
Our max, exactly.
So, you can see these features over
90
00:10:57 --> 00:11:07
here at this plot, right?
So, as this goes to zero,
91
00:11:07 --> 00:11:13
or as N is very large, one over N,
dN/dt goes to zero. And, when N is
92
00:11:13 --> 00:11:19
very small, one over N,
dN/dt is near our max. You're
93
00:11:19 --> 00:11:25
basically growing.
You're over here where the
94
00:11:25 --> 00:11:31
exponential growth curve and the
logistical curve are essentially the
95
00:11:31 --> 00:11:37
same thing. Yeah? Do I
have something wrong?
96
00:11:37 --> 00:11:47
Oh, very good,
very good, very good.
97
00:11:47 --> 00:11:57
Thank you. Absolutely right.
OK, so the slope here is going to
98
00:11:57 --> 00:12:09
be minus r max over K. .
OK, so here we have a nice density
99
00:12:09 --> 00:12:23
dependent response.
OK, let's analyze some more
100
00:12:23 --> 00:12:35
features of this.
Just looking at the exponential and
101
00:12:35 --> 00:12:45
the logistic, just to summarize,
one over N, dN/dt as a function of N,
102
00:12:45 --> 00:12:55
and if we just look at the dN/dt as
a function of N,
103
00:12:55 --> 00:13:06
for exponential we already said that
this is a flat line, right?
104
00:13:06 --> 00:13:14
It's a constant,
but the actual change in numbers as
105
00:13:14 --> 00:13:22
a function of time is a straight
line, whereas for the logistic,
106
00:13:22 --> 00:13:31
one over N, dN/dt as a function of N,
what does this look like?
107
00:13:31 --> 00:13:38
We just did it,
so we are summarizing here.
108
00:13:38 --> 00:13:45
But here's one that I want you to
think about. What does the dN/dt
109
00:13:45 --> 00:13:52
look like as a function of N if
something's growing according to the
110
00:13:52 --> 00:13:59
logistic equation?
Like this? Yes, there you go,
111
00:13:59 --> 00:14:06
like that. Right.
Because there is an inflection point
112
00:14:06 --> 00:14:14
here, right? So,
this is what's sometimes called the
113
00:14:14 --> 00:14:21
optimum yield,
and believe it or not,
114
00:14:21 --> 00:14:29
this model is actually used in
fisheries conservation for years.
115
00:14:29 --> 00:14:36
Now we know that it's so much more
complicated than that that you can't
116
00:14:36 --> 00:14:43
just set the model is.
But one could argue that if you are
117
00:14:43 --> 00:14:50
managing a population that you want
to harvest, that you try to keep
118
00:14:50 --> 00:14:57
them at the density at which the
dN/dt, the production of organisms,
119
00:14:57 --> 00:15:04
is maximal. So, you try to maintain
a population there at that point.
120
00:15:04 --> 00:15:22
One of the features of the logistic
equation is that it assumes
121
00:15:22 --> 00:15:40
instantaneous feedback of the
density on growth rate.
122
00:15:40 --> 00:15:45
In other words,
it says in a population of a certain
123
00:15:45 --> 00:15:50
density, the results in terms of
offspring will be instantaneous.
124
00:15:50 --> 00:15:55
And we know that's not true. So,
this is an oversimplification. Even
125
00:15:55 --> 00:16:00
in the simplest organisms,
even microbes in a culture,
126
00:16:00 --> 00:16:06
say you suddenly starve them up some
substrate that they're using.
127
00:16:06 --> 00:16:10
It takes a while for their
biochemistry to readjust before that.
128
00:16:10 --> 00:16:14
They might have one generation
that's still at the same growth rate
129
00:16:14 --> 00:16:18
as it was before,
before the biochemistry readjusts
130
00:16:18 --> 00:16:22
and says, whoa,
we can't keep going at this rate.
131
00:16:22 --> 00:16:26
Slow down. And then for higher
organisms, you might have a whole
132
00:16:26 --> 00:16:30
generation before that sets it in.
Plants that make seeds, etc.
133
00:16:30 --> 00:16:34
So we know that there's a problem
here. So, people have tried to
134
00:16:34 --> 00:16:39
introduce time lags into the
equation, and we don't have time.
135
00:16:39 --> 00:16:43
I mean there's lots of really neat
things that you can do with this.
136
00:16:43 --> 00:16:48
If this was an advanced ecology
course, you'd be modeling it on your
137
00:16:48 --> 00:16:53
computer, and putting time lags in,
and see what happens and all that
138
00:16:53 --> 00:16:57
kind of stuff.
So we don't have time to do any of
139
00:16:57 --> 00:17:03
that.
I show you this more as a way,
140
00:17:03 --> 00:17:09
I want you to learn how population
ethologists think,
141
00:17:09 --> 00:17:16
not that this is actually the most
important model that ever existed.
142
00:17:16 --> 00:17:22
So how do we introduce time lags
into the logistic?
143
00:17:22 --> 00:17:28
Well, the simplest way is to
introduce time. So, we're
144
00:17:28 --> 00:17:37
going to say dNt/dt.
Let me just make sure that's not
145
00:17:37 --> 00:17:48
ambiguous. dNt/dT,
is equal to r max times N at that
146
00:17:48 --> 00:18:00
time t times K minus
Nt minus tao.
147
00:18:00 --> 00:18:05
In other words,
the density at some time,
148
00:18:05 --> 00:18:10
tao hours or days or whatever,
earlier than t, divided by K. So,
149
00:18:10 --> 00:18:16
what this says is that the growth
rate of the population is a function
150
00:18:16 --> 00:18:21
of the density up a little bit
earlier, or some amount earlier than
151
00:18:21 --> 00:18:27
the time at which we're measuring
the growth rate.
152
00:18:27 --> 00:18:49
So t or tao is the time lag between
sensing environments, and
153
00:18:49 --> 00:19:03
change in growth rate.
So let's look at what that means in
154
00:19:03 --> 00:19:10
terms of, this brings us to another
level of complexity.
155
00:19:10 --> 00:19:17
So let's look at the possibilities
here. So, with no lag,
156
00:19:17 --> 00:19:24
we have our logistic equation,
right? The population just reaches
157
00:19:24 --> 00:19:31
the carrying capacity
and levels off.
158
00:19:31 --> 00:19:38
With a very short lag,
and of course you have to play with
159
00:19:38 --> 00:19:45
this to understand what I mean by
short, long, and medium because you
160
00:19:45 --> 00:19:53
have to change all the different
parameters. But if you have a short
161
00:19:53 --> 00:20:00
lag, what you get is an actual
overshoot of the carrying capacity
162
00:20:00 --> 00:20:08
in the near term because the
feedback hasn't kicked in.
163
00:20:08 --> 00:20:13
But then, it will come back and it
will level off at the carrying
164
00:20:13 --> 00:20:18
capacity. If you have a medium lag,
you will often see something like
165
00:20:18 --> 00:20:23
this where you get a couple of
oscillations in here.
166
00:20:23 --> 00:20:28
But it levels off at the same
carrying capacity.
167
00:20:28 --> 00:20:36
And, a long lag,
you can end up with behavior that
168
00:20:36 --> 00:20:44
ultimately ends up in the population
crashing. And we don't have time to
169
00:20:44 --> 00:20:52
analyze this, but at the end of the
lecture I'm going to come back to
170
00:20:52 --> 00:21:01
why this is so important in terms of
human population growth.
171
00:21:01 --> 00:21:04
And for those of you who are
interested in complex systems and
172
00:21:04 --> 00:21:07
chaos theory, the logistic equation
in its discrete form actually will
173
00:21:07 --> 00:21:10
go chaotic for certain parameter
values. And for a long time,
174
00:21:10 --> 00:21:13
for those of you who don't know what
I'm talking about,
175
00:21:13 --> 00:21:16
just ignore me. And for those who
are interested ought to spend
176
00:21:16 --> 00:21:21
a minute on it.
For a long time,
177
00:21:21 --> 00:21:27
this equation goes into a state of
sort of chaotic oscillations,
178
00:21:27 --> 00:21:33
but that can be described
mathematically.
179
00:21:33 --> 00:21:39
And for a long time,
ecologists kept looking at
180
00:21:39 --> 00:21:45
populations trying to see whether,
indeed, they were growing according
181
00:21:45 --> 00:21:51
to this chaos theory and it hasn't
really developed to anything,
182
00:21:51 --> 00:21:57
but it was interesting. Chaos
theory first started coming to
183
00:21:57 --> 00:22:03
light; the sea collision was one of
the first that people started
184
00:22:03 --> 00:22:09
looking into, coincidentally.
But just because an equation has
185
00:22:09 --> 00:22:13
certain properties,
it doesn't mean that thing it's
186
00:22:13 --> 00:22:18
trying to model has those properties.
So that was a really interesting
187
00:22:18 --> 00:22:23
development. OK,
so let's go back to Pearl and Reed.
188
00:22:23 --> 00:22:27
Where did they go? Oh, they're up
there. OK, so this was
189
00:22:27 --> 00:22:33
all a digression.
So Pearl and Reed were looking at
190
00:22:33 --> 00:22:40
the human population data,
and trying to model it. And they
191
00:22:40 --> 00:22:47
showed that they had this density
dependent response.
192
00:22:47 --> 00:22:53
They developed this equation in
order to describe it.
193
00:22:53 --> 00:23:00
And then, they looked at the data
again using this graphical
194
00:23:00 --> 00:23:07
formulation.
So, let's look at that.
195
00:23:07 --> 00:23:14
We're just going to use the graphic
method, because it's easier to
196
00:23:14 --> 00:23:22
illustrate. And now,
we're looking at the human
197
00:23:22 --> 00:23:29
population in the US,
and this is one over N,
198
00:23:29 --> 00:23:36
dN/dt, and this is N in millions.
And so, they have some data points
199
00:23:36 --> 00:23:44
that they put on here.
This is 1800 to 1810. So,
200
00:23:44 --> 00:23:51
they have different data points for
different intervals,
201
00:23:51 --> 00:23:59
and their last point here was 1900
to 1910, an average of
202
00:23:59 --> 00:24:06
the population size.
And so, they projected down here
203
00:24:06 --> 00:24:12
there were 100 million people then.
So, they said, so they asked the
204
00:24:12 --> 00:24:19
question: OK, we're modeling this
population, we're saying it grows
205
00:24:19 --> 00:24:25
according to the logistic equation,
we can predict what the carrying
206
00:24:25 --> 00:24:32
capacity in the United States for
humans by simply doing a regression
207
00:24:32 --> 00:24:39
through this, and seeing
where it intercepts.
208
00:24:39 --> 00:24:50
So, that should be the carrying
capacity. And they predicted that
209
00:24:50 --> 00:25:02
we'd have 197 million when we reach
the carrying capacity.
210
00:25:02 --> 00:25:08
And that was in the year 2030.
So that was a prediction of their
211
00:25:08 --> 00:25:15
model back in the 1920s,
that the carrying capacity of the US
212
00:25:15 --> 00:25:22
for humans was 197 million,
and that that would be reached in
213
00:25:22 --> 00:25:29
2030. Well, they missed it by a lot.
So, let's look at the data,
214
00:25:29 --> 00:25:37
which is not surprising.
Here's 1965. We reached 200 million
215
00:25:37 --> 00:25:47
way before 2030.
1990, 250 million,
216
00:25:47 --> 00:25:56
and actually today, at 10:45 this
morning, because I looked it up on
217
00:25:56 --> 00:26:06
my trusty population
clock on the Web,
218
00:26:06 --> 00:26:13
we had 295,979,
38 people. This is also done by
219
00:26:13 --> 00:26:20
modeling, we're not counting people
one at a time.
220
00:26:20 --> 00:26:27
But this website is keeping track
based on various models.
221
00:26:27 --> 00:26:34
And, based on the models that we
have today, in 2030 we should have
222
00:26:34 --> 00:26:41
about 345 million.
But these models are based on
223
00:26:41 --> 00:26:47
something entirely much more complex
now than the simple logistic
224
00:26:47 --> 00:26:53
equation. OK,
so the contribution of Pearl and
225
00:26:53 --> 00:26:59
Reed was to be yet to get people to
start thinking about the feedback
226
00:26:59 --> 00:27:05
mechanisms, how to model population
growth, and think about the feedback
227
00:27:05 --> 00:27:11
mechanisms in that model.
You don't have that in your handout,
228
00:27:11 --> 00:27:18
but it's not important. It's not on
the web, but if you care about it,
229
00:27:18 --> 00:27:24
there is the website that keeps
track of human population in the US.
230
00:27:24 --> 00:27:31
So, here's the total population
number that I got this morning at
231
00:27:31 --> 00:27:37
10:14 and 17 seconds off the web.
And these are just some interesting
232
00:27:37 --> 00:27:43
statistics for the US,
and I have them for the last three
233
00:27:43 --> 00:27:48
years: one birth every eight seconds,
one death every 13 seconds,
234
00:27:48 --> 00:27:54
one migrant every 26 seconds,
and a net gain of one person every
235
00:27:54 --> 00:28:00
12 seconds. So they're keeping
close track here.
236
00:28:00 --> 00:28:04
OK, all right,
so now are going to move on to
237
00:28:04 --> 00:28:08
global population growth,
humans on the earth, the whole shoot
238
00:28:08 --> 00:28:12
and match. And,
there's this wonderful book for
239
00:28:12 --> 00:28:17
anyone who's interested by Joel
Cohen, called,
240
00:28:17 --> 00:28:21
How Many People Can the Earth
Support? And,
241
00:28:21 --> 00:28:25
it's a great book for MIT students
because it's a wonderfully nerdy
242
00:28:25 --> 00:28:30
account. I'm a nerd,
so I can say that.
243
00:28:30 --> 00:28:35
I'm a total nerd.
But it's just a wonderful account,
244
00:28:35 --> 00:28:40
analysis, if you analyze human
population growth,
245
00:28:40 --> 00:28:45
and at the same time looking at the
phenomenon in a totally objective
246
00:28:45 --> 00:28:50
way. He's a theoretical ecologist.
So, this is in your textbook. But,
247
00:28:50 --> 00:28:55
it's from this book. And, it's from
10,000 B.C. up to here we are today,
248
00:28:55 --> 00:29:01
the population on Earth in billions.
249
00:29:01 --> 00:29:06
And, this is back in the hunter
gatherer era. We had 4 million
250
00:29:06 --> 00:29:11
people. And this was a small
revolution at the time,
251
00:29:11 --> 00:29:16
the introduction of the agriculture
and domestication of animals allowed
252
00:29:16 --> 00:29:21
for higher birth rates,
and so had a little blip,
253
00:29:21 --> 00:29:26
went up to 7 million here.
And then for a long time, there was
254
00:29:26 --> 00:29:32
just no change in human
population on Earth.
255
00:29:32 --> 00:29:38
And so then, here you start to get,
I'm not sure what started this up
256
00:29:38 --> 00:29:44
rise. Maybe when we see the next
slide we'll see.
257
00:29:44 --> 00:29:51
No, I'm not sure what started that.
We'll have to look into that.
258
00:29:51 --> 00:29:57
Maybe just the accumulation of
people that you can't see on this
259
00:29:57 --> 00:30:04
scale, here's the bubonic
plague, a decrease.
260
00:30:04 --> 00:30:08
Here's the beginning of the
Industrial Revolution and the
261
00:30:08 --> 00:30:13
introduction of modern medicine,
which greatly reduced mortality. So,
262
00:30:13 --> 00:30:18
you see this incredible,
and here's fossil fuel, increase in
263
00:30:18 --> 00:30:23
the population of humans on Earth.
So, if you look at this curve, you
264
00:30:23 --> 00:30:28
think, oh my God,
we're in the middle of this
265
00:30:28 --> 00:30:33
incredible exponential increase.
And, the reality is this doesn't fit
266
00:30:33 --> 00:30:37
at all in an exponential model at
all. I mean, if you tried to fit
267
00:30:37 --> 00:30:42
that to our simple exponential,
it does not fit. We are going to
268
00:30:42 --> 00:30:47
explain what's happening here in a
minute. So here we are at 6 billion
269
00:30:47 --> 00:30:51
people. And we hit 6 billion in
1999. And here we are with a steady
270
00:30:51 --> 00:30:56
increase. I've just got the last
three years. This marks the
271
00:30:56 --> 00:31:01
lectures that I've given
in this class.
272
00:31:01 --> 00:31:05
Every year I check in and see where
we are. It's kind of a living
273
00:31:05 --> 00:31:09
document. And,
we're now projected to reach 9
274
00:31:09 --> 00:31:13
billion and level off.
When I first started teaching about
275
00:31:13 --> 00:31:17
human population growth,
the projections were at 12 billion.
276
00:31:17 --> 00:31:21
And I'm not that old. This number
keeps changing,
277
00:31:21 --> 00:31:25
and luckily it's changing in the
right direction.
278
00:31:25 --> 00:31:29
We keep predicting fewer and fewer
humans before it will level off.
279
00:31:29 --> 00:31:33
But it's still 3 billion more humans
than we have now,
280
00:31:33 --> 00:31:38
and many people think now were
already beyond the carrying capacity
281
00:31:38 --> 00:31:42
of the Earth. So,
I'm not saying not to worry,
282
00:31:42 --> 00:31:47
I'm just saying that at least it's
going in the right direction.
283
00:31:47 --> 00:31:51
So, in Cohen's book, he analyzes
this, sort of the history of humans
284
00:31:51 --> 00:31:56
on Earth as having four major
evolutionary changes where you have
285
00:31:56 --> 00:32:00
the dramatic change in population
growth. You have local agriculture
286
00:32:00 --> 00:32:05
in 8000 B.C.
And, the doubling time of the
287
00:32:05 --> 00:32:11
population before and after those
evolutions went from what he
288
00:32:11 --> 00:32:16
estimates to be 40,
00 to 300,000 years for a population
289
00:32:16 --> 00:32:21
to double down to 1000 to 3000 years
for the population to double.
290
00:32:21 --> 00:32:27
In other words, this is an
incredibly faster growth rate,
291
00:32:27 --> 00:32:32
because this is doubling times.
And then, with global agriculture in
292
00:32:32 --> 00:32:37
the 1700s, again you have a
shortening of the doubling time of
293
00:32:37 --> 00:32:42
the population.
And then in the 50s with the
294
00:32:42 --> 00:32:47
introduction of real public health
across the world,
295
00:32:47 --> 00:32:52
another reduction,
and luckily in the 70s,
296
00:32:52 --> 00:32:57
with the introduction of fertility
control, at least in the developed
297
00:32:57 --> 00:33:03
countries, is the first time you
actually see a shift.
298
00:33:03 --> 00:33:08
We've gone from growing faster,
and faster, and faster to actually
299
00:33:08 --> 00:33:14
growing more slowly.
The doubling time is extending.
300
00:33:14 --> 00:33:20
So, the good news is we're not in
some kind of runaway population
301
00:33:20 --> 00:33:26
growth that's going to continue
forever. We've already peaked out
302
00:33:26 --> 00:33:32
as a globe, and we are going to
level off in terms humans.
303
00:33:32 --> 00:33:37
And the real big question is when we
level off, will we be above the
304
00:33:37 --> 00:33:43
carrying capacity of the Earth?
Have we overshot K? And we don't
305
00:33:43 --> 00:33:49
know yet because these feedback
mechanisms haven't come back.
306
00:33:49 --> 00:33:55
So, let's now analyze this a little
bit more before we look at it in
307
00:33:55 --> 00:34:01
that context, because this
is an important thing.
308
00:34:01 --> 00:34:05
First of all, before we do that,
I want to remind you that all of
309
00:34:05 --> 00:34:09
these lectures are tied together
because remember this from lecture
310
00:34:09 --> 00:34:14
20 when we were talking about
biogeochemical cycles?
311
00:34:14 --> 00:34:18
And, here's the same population
size and billions on Earth,
312
00:34:18 --> 00:34:23
the brown curve. It's smoothed over,
and these are the greenhouse gases,
313
00:34:23 --> 00:34:27
concentration of greenhouse gases in
the atmosphere. This is
314
00:34:27 --> 00:34:32
the human footprint.
This is how we've changed the
315
00:34:32 --> 00:34:38
metabolism of the Earth,
by this explosive growth of humans.
316
00:34:38 --> 00:34:44
And one more slide just showing you
that this is another way to look at
317
00:34:44 --> 00:34:49
it, showing that the growth of the
global population has peaked.
318
00:34:49 --> 00:34:55
So, over here, each of these is the
population in billions,
319
00:34:55 --> 00:35:01
and it basically shows you the
number of years necessary
320
00:35:01 --> 00:35:06
to add a billion.
And you could see that it's taking
321
00:35:06 --> 00:35:11
longer and longer to add a billion.
You can see that there is an
322
00:35:11 --> 00:35:16
inflection point here.
So, using the tools that we've
323
00:35:16 --> 00:35:22
developed to analyze populations,
let's look at why this growth is
324
00:35:22 --> 00:35:27
leveling off. What caused the
growth to begin with,
325
00:35:27 --> 00:35:32
and why it's leveling off?
And the really important feature
326
00:35:32 --> 00:35:38
here is what's called a demographic
transition. This is what we are
327
00:35:38 --> 00:35:44
going through on the Earth right now
in terms of human population growth.
328
00:35:44 --> 00:35:50
And, the way we look at this, we
are planning birth rates here,
329
00:35:50 --> 00:35:56
which is the pink one, and death
rate here, which is the green one.
330
00:35:56 --> 00:36:02
And, when birth rates and death
rates are both uniformly high,
331
00:36:02 --> 00:36:08
which is the way it was back in the
early days when we didn't have
332
00:36:08 --> 00:36:14
fertility control,
and we didn't have modern medicine.
333
00:36:14 --> 00:36:17
So, you had a lot of babies and a
lot of people dying.
334
00:36:17 --> 00:36:21
And growth rate, and so this is the
total population.
335
00:36:21 --> 00:36:24
So, you don't have much population
growth. Then,
336
00:36:24 --> 00:36:28
what happens, you get to a place
where you have a very
337
00:36:28 --> 00:36:32
high birth rate.
Birth rate continues to stay high,
338
00:36:32 --> 00:36:38
but with the introduction of public
health, and modern medicine,
339
00:36:38 --> 00:36:43
we were able to keep people alive a
lot longer. And,
340
00:36:43 --> 00:36:49
that came in advance of fertility
control. So, what happens,
341
00:36:49 --> 00:36:54
when these two curves deviate from
one another, you have explosive
342
00:36:54 --> 00:37:00
growth, and that's what this big
exponential shoot is.
343
00:37:00 --> 00:37:04
But then, if you then reduce the
birth rates through fertility
344
00:37:04 --> 00:37:09
control to match the death rates,
you then have low birth rates and
345
00:37:09 --> 00:37:14
low death rates.
Then you have no population growth,
346
00:37:14 --> 00:37:19
OK? So, it's very simple and
intuitive when you understand what's
347
00:37:19 --> 00:37:24
going on, but I don't think that
most people really have come to the
348
00:37:24 --> 00:37:29
point of thinking about
it like that.
349
00:37:29 --> 00:37:37
And where we are on Earth today is
the developed countries have gone
350
00:37:37 --> 00:37:46
through their demographic transition.
And you have a sense of that just
351
00:37:46 --> 00:37:55
from looking at family size in these
countries. So,
352
00:37:55 --> 00:38:04
if we look at, this is Sweden as an
example of a developed country.
353
00:38:04 --> 00:38:10
And this was 1800.
And this is 2000. You see
354
00:38:10 --> 00:38:16
something like this.
This is just an approximation.
355
00:38:16 --> 00:38:22
This is the birth rate and this is
the death rate,
356
00:38:22 --> 00:38:28
and the population growth rate looks
something like this.
357
00:38:28 --> 00:38:36
The populations leveled off whereas
if you look at a country like Egypt
358
00:38:36 --> 00:38:44
over the same time frame,
and you can get these curves off the
359
00:38:44 --> 00:38:52
web easily, it looks something like
this. You have a high
360
00:38:52 --> 00:38:59
birth rate.
And death rate has gone down,
361
00:38:59 --> 00:39:05
but they're not matching each other
at all. So, population look
362
00:39:05 --> 00:39:11
something like this.
It hasn't even begun to level off.
363
00:39:11 --> 00:39:17
So the real trick is, in terms of
trying to level off at someplace
364
00:39:17 --> 00:39:23
lower than 9 billion,
is to get the birthrates in the
365
00:39:23 --> 00:39:29
developing countries to drop
as fast as we can.
366
00:39:29 --> 00:39:35
And that will determine the level at
which humans will level off on Earth.
367
00:39:35 --> 00:39:41
So, let's just briefly,
let me go back over here,
368
00:39:41 --> 00:39:47
and let's go back over this carrying
capacity. And this is basically
369
00:39:47 --> 00:39:53
what Joel Cohen's book is about,
where he says, how many people can
370
00:39:53 --> 00:39:59
the Earth support?
He's asking, what's the carrying
371
00:39:59 --> 00:40:05
capacity of the earth for humans?
And here are the possibilities.
372
00:40:05 --> 00:40:13
And of course, I'm simplifying the
most complex system that we know
373
00:40:13 --> 00:40:20
into a simple two-dimensional graph,
but I think it's a good way to think
374
00:40:20 --> 00:40:28
about it. Here's the way we've been
living on Earth.
375
00:40:28 --> 00:40:34
We have been growing like this.
Granted, we're starting to level
376
00:40:34 --> 00:40:40
off, but we've been growing like
this. And what we've been assuming,
377
00:40:40 --> 00:40:47
is that the carrying capacity will
grow with us, OK?
378
00:40:47 --> 00:40:53
We can handle as many humans as we
want to put because we,
379
00:40:53 --> 00:41:00
smart people, with technology can
increase the carrying capacity.
380
00:41:00 --> 00:41:05
If we don't have enough grain,
we'll genetically engineer to make
381
00:41:05 --> 00:41:10
more grain. We can fix it; we can
fix it, so let's just go with the
382
00:41:10 --> 00:41:15
flow. And indeed,
technology has greatly increased the
383
00:41:15 --> 00:41:20
carrying capacity of the earth for
humans. There's no doubt about it.
384
00:41:20 --> 00:41:25
But there's got to be a limit. So,
is this the model that we want to go
385
00:41:25 --> 00:41:30
by? So, some people argue,
so, the climate, we'll fix that with
386
00:41:30 --> 00:41:35
technology.
We can fix any of this with
387
00:41:35 --> 00:41:40
technology, and if things get really
bad, we'll go to Mars; we'll
388
00:41:40 --> 00:41:45
terraform Mars.
We'll colonize planets.
389
00:41:45 --> 00:41:49
That's not that far-fetched,
so why should we worry about all
390
00:41:49 --> 00:41:54
these humans on the Earth?
We'll just figure out, we'll go out
391
00:41:54 --> 00:41:59
and find new places.
So that's one model.
392
00:41:59 --> 00:42:04
Another model is, if we're going to
do this, here's what I call the
393
00:42:04 --> 00:42:12
optimistic model.
Well, I guess this is the super
394
00:42:12 --> 00:42:22
optimistic model.
This one assumes that it'll do
395
00:42:22 --> 00:42:33
something like this that we may
overshoot. And then birth rates,
396
00:42:33 --> 00:42:37
and if you want to you can easily
describe a scenario that says that
397
00:42:37 --> 00:42:42
we have overshot,
that this whole environmental
398
00:42:42 --> 00:42:46
movement, the measurement of toxins
in our environment,
399
00:42:46 --> 00:42:51
the global change, all of that is
really overshooting the carrying
400
00:42:51 --> 00:42:56
capacity. And we wouldn't be
worrying about things that we're
401
00:42:56 --> 00:43:00
worrying about if we hadn't overshot
it, but that if we get
402
00:43:00 --> 00:43:07
our act together,
we won't have eroded the Earth's
403
00:43:07 --> 00:43:15
natural system so much that we can
come back to a stable level.
404
00:43:15 --> 00:43:23
And then, of course, the
pessimistic scenario is that,
405
00:43:23 --> 00:43:31
indeed, we've overshot, and we've
overshot so much that we have eroded
406
00:43:31 --> 00:43:38
the carrying capacity,
and that we will level off at some
407
00:43:38 --> 00:43:44
level that the Earth will no longer
be able to support the level of
408
00:43:44 --> 00:43:50
humans that it can even support now,
that we have lost so much topsoil,
409
00:43:50 --> 00:43:56
and modern agriculture won't be able
to overcome that,
410
00:43:56 --> 00:44:02
that our water will be polluted,
that the climate will change so
411
00:44:02 --> 00:44:08
dramatically, the fisheries will be
eliminated, yada, yada, yada.
412
00:44:08 --> 00:44:13
I shouldn't say yada,
yada, yada. Those are catastrophic
413
00:44:13 --> 00:44:19
things. Erase that from the tape!
Every once in a while,
414
00:44:19 --> 00:44:25
I remember I'm being taped.
So, those are bad things, not to be
415
00:44:25 --> 00:44:30
yada, yada, yada'd.
So, anyway, this is what some people
416
00:44:30 --> 00:44:35
are worried about,
that we are, indeed right now,
417
00:44:35 --> 00:44:40
in your lifetime and in fact mostly
in your lifetime,
418
00:44:40 --> 00:44:45
you are inheriting this,
notice the time frames on this graph.
419
00:44:45 --> 00:44:50
I mean, this is just this little
snippet of time in the history of
420
00:44:50 --> 00:44:55
life on Earth where all these
dramatic things are happening.
421
00:44:55 --> 00:45:00
And we just happen to be living in
it.
422
00:45:00 --> 00:45:04
Just think if you're living back
here, and thousands and thousands of
423
00:45:04 --> 00:45:08
years went by,
and nothing changed.
424
00:45:08 --> 00:45:12
OK, so we don't have any answers,
but this is a way to think about it,
425
00:45:12 --> 00:45:16
and a lot of people are putting a
lot of energy into modeling the
426
00:45:16 --> 00:45:20
systems, and try to figure out where
we are the scariest trajectories.
427
00:45:20 --> 00:45:24
So, the next two lectures Professor
Martin Polz, who is a professor in
428
00:45:24 --> 00:45:28
civil and environmental engineering,
and the microbiologist is going to
429
00:45:28 --> 00:45:33
come in and talk to you about,
again, its population economy.
430
00:45:33 --> 00:45:37
He'll talk to you about population
genetics, and some really exciting
431
00:45:37 --> 00:45:42
work that's going on in the field
now using genomics to decipher
432
00:45:42 --> 00:45:46
evolution and population biology.
And then I'll be back with some
433
00:45:46 --> 00:45:49
really neat DVD clips.
So, come back.